=10a^2-27ab+5b^2

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Solution for =10a^2-27ab+5b^2 equation: 


Simplifying
0 = 10a2 + -27ab + 5b2

Reorder the terms:
0 = -27ab + 10a2 + 5b2

Solving
0 = -27ab + 10a2 + 5b2

Solving for variable 'a'.
Remove the zero:
27ab + -10a2 + -5b2 = -27ab + 10a2 + 5b2 + 27ab + -10a2 + -5b2

Reorder the terms:
27ab + -10a2 + -5b2 = -27ab + 27ab + 10a2 + -10a2 + 5b2 + -5b2

Combine like terms: -27ab + 27ab = 0
27ab + -10a2 + -5b2 = 0 + 10a2 + -10a2 + 5b2 + -5b2
27ab + -10a2 + -5b2 = 10a2 + -10a2 + 5b2 + -5b2

Combine like terms: 10a2 + -10a2 = 0
27ab + -10a2 + -5b2 = 0 + 5b2 + -5b2
27ab + -10a2 + -5b2 = 5b2 + -5b2

Combine like terms: 5b2 + -5b2 = 0
27ab + -10a2 + -5b2 = 0

Factor a trinomial.
(-5a + b)(2a + -5b) = 0


Subproblem 1
Set the factor '(-5a + b)' equal to zero and attempt to solve:

Simplifying
-5a + b = 0

Solving
-5a + b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
-5a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-5a + 0 = 0 + -1b
-5a = 0 + -1b
Remove the zero:
-5a = -1b

Divide each side by '-5'.
a = 0.2b

Simplifying
a = 0.2b

Subproblem 2
Set the factor '(2a + -5b)' equal to zero and attempt to solve:

Simplifying
2a + -5b = 0

Solving
2a + -5b = 0

Move all terms containing a to the left, all other terms to the right.

Add '5b' to each side of the equation.
2a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
2a + 0 = 0 + 5b
2a = 0 + 5b
Remove the zero:
2a = 5b

Divide each side by '2'.
a = 2.5b

Simplifying
a = 2.5b
Solution
a = {0.2b, 2.5b}

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